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\@writefile{toc}{\contentsline {section}{\numberline {IV}Particle Tracking Velocimetry}{7}}
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces This shows how the PTV algorithm works on an example particle in a set of images.}}{7}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces The graphical user interface\nobreakspace  {}(\unhbox \voidb@x \hbox {V-B}\hbox {}) we developed for the project that allowed us to easily define all of the necessary parameters to fine tune the execution of the two methods for tracking particles. Within the program, you can see a frame with its particles and corresponding overlayed velocities.}}{9}}
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\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces The graphical output of the PTV algorithm when tracking 241 particles, each moving to the right with a velocity of 10 pixels per frame. Notice how the algorithm gets occationally confused and mislinks the particles (non-horizontal lines). This is due to random alignment of unrelated particles with the secondary search radius. The PTV algorithm chooses the first extended link it finds since it is fairly unlikely another particle will meet the same conditions. In higher density fields, however, this can cause occational errors.}}{10}}
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces The graphical output of the PIV algorithm when tracking 241 particles, each moving to the right with a velocity of 10 pixels per frame. Without periodicity in the spacing of particles, the PIV algorithm is very accurate for such a simple velocity field. Errors are most likely generated at the edges of the image or in regions where no particles exist, since velocities are still chosen, even if the cross correlation just returns near zero values on the order of roundoff error.}}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {VII}Performance Expectations for PIV and PTV and Test Case Imagery}{10}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces In this actual ultrasound images, the PTV algorithm performs well in the low-density, slow moving particle areas to the lower right. It has trouble producing intelligible velocities for the high-density, fast-moving particle regions in the corners of the images.}}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces In this actual ultrasound images, the PIV algorithm performs just as well in the low-density, slow moving particle areas to the lower right. It also has trouble producing intelligible velocities for the high-density, fast-moving particle regions in the corners of the images.}}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces A fundamental assumption of the PTV algorithm is the movement of particles in a linear fashion. Small secondary search radius $R_2$ are thus unable to locate the correct location of particles on a curved path. The secondary radius size can be increased, but this can cause false linkages.}}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces This illustrates one of the major flaws with the PTV method. Given a grid-like arrangement of particles, the algorithm is incapable of determining which path is the true path without some intelligent inferences and history that are not present in this na\"{i}ve implementation. Above, the highlighted portions are examples of the problem. The below figure illustrates what is happening over the three frames.}}{11}}
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\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces The PTV algorithm is able to accurately determine the velocites of each particle in this frame as they rotate. Those particles on the outside are rotating faster, orbiting around the center, stationary particle.}}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces The PIV algorithm handles this rotation instance without any problems, as well.}}{13}}
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